3. The attempt at a solution
a.) would you do the power rule for this? 2tanx
b.) this is a combination of the chain rule and the power rule?
-3sinx2*2x
c.) use the quotient rule
((5x+2)(2)-(2x-1)(5))/(5x+2)2

((10x+2)-(10x-5))/(5x+2)2

7/(5x+2)2

d.) use the chain rule and the product rule?
Use the chain rule for the first pararenthasis. And then use the product rule?
f.) used the chain rule
2sinxcosx*(-cosxsinx)

a) this is actually both chain and product rule. tan[itex]^{2}[/itex]x is the same as (tanx)[itex]^{2}[/itex].
So now you use power rule on the entire function, multiplied by the derivative of the function, i.e. 2tanxsec[itex]^{2}[/itex]x

b) Again, chain rule and power rule. cos[itex]^{3}[/itex](x[itex]^{2}[/itex]) can be rewritten as (cos(x[itex]^{2}[/itex]))[itex]^{3}[/itex], which, when differentiated, becomes
3(cos(x[itex]^{2}[/itex]))[itex]^{2}[/itex](-sin(x[itex]^{2}[/itex]))(2x)

c) Looks right

d) yes

e) Combination quotient rule / power rule / chain rule. first differentiate as if it were a single variable, then differentiate what's inside using quotient rule.

f) the first part looks right, 2sinxcosx, but the 2nd part doesn't. The 2nd part should basically be (d/dx)(sinxcosx) which is product rule, i.e. cos[itex]^{2}[/itex]x - sin[itex]^{2}[/itex]x

Staff: Mentor

a) this is actually both chain and product rule. tan[itex]^{2}[/itex]x is the same as (tanx)[itex]^{2}[/itex].
So now you use power rule on the entire function, multiplied by the derivative of the function, i.e. 2tanxsec[itex]^{2}[/itex]x

b) Again, chain rule and power rule. cos[itex]^{3}[/itex](x[itex]^{2}[/itex]) can be rewritten as (cos(x[itex]^{2}[/itex]))[itex]^{3}[/itex], which, when differentiated, becomes
3(cos(x[itex]^{2}[/itex]))[itex]^{2}[/itex](-sin(x[itex]^{2}[/itex]))(2x)

c) Looks right

d) yes

e) Combination quotient rule / power rule / chain rule. first differentiate as if it were a single variable, then differentiate what's inside using quotient rule.

f) the first part looks right, 2sinxcosx, but the 2nd part doesn't. The 2nd part should basically be (d/dx)(sinxcosx) which is product rule, i.e. cos[itex]^{2}[/itex]x - sin[itex]^{2}[/itex]x

Don't provide solutions here in the future. It violates the PF rules that you agreed to when you joined here.